Nearly a dozen Republican pollsters gathered Wednesday morning for a long-scheduled event to deliver survey results funded by a lobbying effort for the House to pass a comprehensive immigration overhaul — but they were forced to reconcile their findings with House Majority Leader Eric Cantor’s primary defeat Tuesday night.

In a Capitol Hill hotel ballroom, the pollsters, whose collective client lists include a majority of Republicans in Congress, went through the two polls they conducted of Hispanic voters and of the electorate at-large for FWD.us, a pro-immigration overhaul, tech-community lobbying group founded by Facebook CEO Mark Zuckerberg.

It’s a two-pronged argument that highlights the importance of congressional action on immigration for the party’s ability to win national elections and reassures Republicans they should not fear repercussions at the primary ballot box.

While Cantor’s stunning loss was to a challenger who based part of his message attacking the No. 2 House Republican on that issue, the pollsters explained that was in fact not the race from Tuesday night that should be used to judge immigration’s electoral power. Whit Ayres, who has previously highlighted the dire state of the party’s appeal to Hispanic voters , said the resounding victory of Sen. Lindsey Graham, R-S.C., who was a central proponent of the Senate immigration effort, over a handful of conservative challengers was a more telling indicator.

“That is a much better test of how this issue plays out in a Republican primary and much better reflection of the numbers you see here than anything that happened in Virginia’s 7th District,” said Ayres, a partner at North Star Opinion Research.

Beyond that, the central theme is that with the share of white voters on a steady decline, Republicans cannot win another presidential election with 27 percent support among Hispanics — which is what Romney took against President Barack Obama in 2012. The argument is that passing immigration legislation not only offers a solution to the problem of 11 million undocumented people living in the country, it also gives the GOP an opening with a significant number of voters in the fastest-growing demographic group.

“We’re likely to have a good election in 2014, which as a Republican I think is great,” said Rob Jesmer, a veteran GOP operative and consultant to FWD.us. “But we’re going to wake up again on Jan. 1 in a presidential cycle and we’re all going to be staring at ourselves wondering about the disaster of Hillary Clinton being president. At some point we have to deal with this.”

There was a long pause when the pollsters, all sitting in a line behind a long table, were asked whether they had shared this data with their congressional clients. Ayres said he did, while B.J. Martino of the Tarrance Group noted they don’t advise their clients on what to believe.

“We are primarily working to help them in races,” Martino said. “Every member is different, but our advice and recommendations here is that for the longtime viability and success for our party this is the road we need to be headed down.”

Based on their polling, the group of pollsters argued that when a comprehensive immigration overhaul package is explained accurately, two-thirds of Republican voters across the party spectrum favored the proposal and would continue to support a candidate who voted for it.

In fact, by a 70 percent to 21 percent margin, Republican voters would support a candidate in favor of the immigration plan over a candidate who opposed it.

In explaining the numbers, Jon Lerner of Basswood Research was forced to deviate from the poll to clarify why Cantor’s loss was not inconsistent with their findings. Lerner said there isn’t any evidence yet that immigration was the driving issue in Cantor’s race and that in no race he’s worked on that featured a tea party challenger has it been a central issue.

“I’m not being entirely dismissive of it in the Cantor case, I would just suggest to you that it’s probably too pat an answer to say that immigration played a big role in it,” Lerner said. “Our data here does suggest that Republican candidates who support the immigration reform issue properly have relatively little to fear in Republican primaries.”

Jesmer, a former executive director at the National Republican Senatorial Committee, noted that House members in safe districts may not have to worry about increasing their support. But if the party is going to make significant policy changes, it has to be able to win national elections.

“Single women, married women, independents — in all those subgroups, our vote share goes up if we pass this,” Jesmer said. “I think there’s not enough members who feel that and need those people to win. But you have governors, you have senators, you have state legislators, people up and down the ticket who are very dependent on this.”